Both sides struggled to find attacking rythym in a game played in 31-degree heat and punctuated by additional drinks breaks.
Union’s American striker Jordan Siebatcheu was withdrawn in the 70th minute after failing to keep his early season scoring streak alive, with the summer arrival having found the net in both of Berlin’s games so far this season.
Mainz went close with the only notable chance of the first half, when an attempted cross from Jae-sung Lee was swatted to safety by Union keeper Frederik Roennow.
Rani Khedira had a chance to put Union in the lead in the 59th minute but dragged his low shot just wide.
Mainz’s Austrian striker Marlon Mustapha, subbed on in the 75th minute, had an immediate impact, causing problems for a tiring Union defence and having two clear chances on goal.
Mainz had a chance in the 90th minute when Dutch striker latched onto a loose ball in the penalty area, but Union defender Robin Knoche shouldered the ball away from the goal to safety.
The result sees both sides finish the round with four points.
Union have now gone a club record nine Bundesliga matches without a loss, winning seven and drawing two since they last tasted defeat, against Bayern Munich in March.
In Sunday’s final game, Bayern will have the chance to reclaim top spot on the ladder when they welcome former coach Niko Kovac’s Wolfsburg to the Allianz Arena.